A mathematical model of the early visual system and border completion via subriemannian Hamiltonian geodesics

In this thesis, we aim to discuss a simple mathematical model for the edge detection mechanism and the boundary completion problem in the human brain in a differential geometry framework. We describe the columnar structure of the primary visual cortex as the fiber bundle R2 × S1, the orientation bundle, and by introducing a first vector field on it, explain the edge detection process. Edges are detected through a lift from the domain in R2 into the manifold R2 × S1 and are horizontal to a completely non-integrable distribution. Therefore, we can construct a subriemannian structure on the manifold R2 × S1, through which we retrieve perceived smooth contours as subriemannian geodesics, solutions to Hamilton’s equations. To do so, in the first chapter, we illustrate the functioning of the most fundamental structures of the early visual system in the brain, from the retina to the primary visual cortex. We proceed with introducing the necessary concepts of differential and subriemannian geometry in chapters two and three. We finally implement our model in chapter four, where we conclude, comparing our results with the experimental findings of Heyes, Fields, and Hess on the existence of an association field.

Design and implementation of BIRDY satellite data and Radiation Payload simulators

Numerical modelling and simulations are needed to develop and test specific analysis methods by providing test data before BIRDY would be launched. This document describes the "satellite data simulator" which is a multi-sensor, multi-spectral satellite simulator produced especially for the BIRDY mission which could be used as well to analyse data from other satellite missions providing energetic particles data in the Solar system.

Estimation of the satellite ephemerides of Saturn using optical navigation pictures of Cassini

The goal of this dissertation thesis is the estimation of the Saturnian satellites ephemerides using optical data of Cassini. In the first part we describe the software employed for the reduction of the images showing its main features and the accuracy that can be achieved comparing the results with published astrometry. Afterwards we describe the orbit determination problem (ODP) with particular focus on the weights selection for the estimation process. The third chapter describes the dynamical model used and the sources of potential errors in the residuals. The model have been validated trying to replicate JPL's published ephemerides SAT365, SAT375, SAT389 and SAT409. The final part investigates the residuals and the estimated ephemerides with particular focus on the giant moon Titan, the only in the solar system with an atmosphere other than the Earth. No astrometry have been retrieved in literature of Titan using optical observables, thus this represents one of the first investigations of the giant.

Study of the rotational state of Titan using radio tracking data of the Dragonfly mission

Our solar system contains an impressive amount of celestial bodies. For example Saturn posses a huge variety of natural satellites, the diversity in size and physical proprieties of which might amaze imagination. The observational data gathered in 30 years range of deep space missions revealed, that some of these bodies can hide subsurface oceans under their crust. The water, as we know, serves as a fundamental base for a possible appearance of life. This statement is quite exited for the scientific society and serves as a reason for studying so called ”ocean worlds”. In order to detect the celestial bodies with the hidden subsurface ocean, one of the key aspects is the study of their rotational state, which is strongly coupled with the body internal structure. It can be done through the various techniques mentioned in Chapter 1. The main goal of the thesis is the study of rotational state of Titan, whose interior structure expectedly contains liquid ocean layer under its icy crust. Titan is the largest moon of Saturn and it is the second largest moon in the solar system in general. This natural satellite is of particular scientific interest, because it is one of a kind which has substantial atmosphere. The present work was done using radio tracking data of the Dragonfly mission which is one of the next NASA’s missions destined for Titan selected as a part of the New Frontiers Program in 2019. The detailed characteristic of the Dragonfly regarding the landing site and mission lifetime was reported in Chapter 2. The radio-tracking communication link from Titan side was performed using Dragonfly X band transponder according to the schedule tracking opportunity. From Earth side according to the mission, Deep Space Station 25 which is a part of NASA’s Deep Space Network was considered. Only Doppler data was used for studying Titan rotational state, even though there are other reliable techniques described in Chapter 3, that in general could be implemented.

Efficiency limits for silicon/perovskite tandem solar cells: a theoretical model

The primary goal of this work is related to the extension of an analytic electro-optical model. It will be used to describe single-junction crystalline silicon solar cells and a silicon/perovskite tandem solar cell in the presence of light-trapping in order to calculate efficiency limits for such a device. In particular, our tandem system is composed by crystalline silicon and a perovskite structure material: metilammoniumleadtriiodide (MALI). Perovskite are among the most convenient materials for photovoltaics thanks to their reduced cost and increasing efficiencies. Solar cell efficiencies of devices using these materials increased from 3.8% in 2009 to a certified 20.1% in 2014 making this the fastest-advancing solar technology to date. Moreover, texturization increases the amount of light which can be absorbed through an active layer. Using Green’s formalism it is possible to calculate the photogeneration rate of a single-layer structure with Lambertian light trapping analytically. In this work we go further: we study the optical coupling between the two cells in our tandem system in order to calculate the photogeneration rate of the whole structure. We also model the electronic part of such a device by considering the perovskite top cell as an ideal diode and solving the drift-diffusion equation with appropriate boundary conditions for the silicon bottom cell. We have a four terminal structure, so our tandem system is totally unconstrained. Then we calculate the efficiency limits of our tandem including several recombination mechanisms such as Auger, SRH and surface recombination. We focus also on the dependence of the results on the band gap of the perovskite and we calculare an optimal band gap to optimize the tandem efficiency. The whole work has been continuously supported by a numerical validation of out analytic model against Silvaco ATLAS which solves drift-diffusion equations using a finite elements method. Our goal is to develop a simpler and cheaper, but accurate model to study such devices.